1. Field of the Invention
The invention relates to a method and to means for determining the shape of a rough surface of an object. The invention further relates to a coordinate measurement machine comprising such means. Additionally the invention relates to an optical element and a mandrel for manufacturing an optical element. Further, the invention relates to a method for calibrating means for determining the shape of a rough surface of an object.
A rough or a matt surface in this context is in contrast to a smooth surface a surface, which appears matt when being illuminated from at least one angle of incidence with light having a given wavelength λ. The roughness related height variation of such a surface is typically around λ/4 or more. Light reflected off the surface then has a phase shift variation of λ/2, causing destructive interference in the reflected light. Rough or matt surfaces referred to in this application can be ground, abraded or lapped pre-stages of polished surfaces, as used in optical systems. Also optical devices in their final from, like scattering discs, diffusors or visual displays can have rough surfaces. Materials used for such objects can be glasses, including fused silica, crystals like calcium fluoride or glass ceramics like Zerodur, ULE or Sital.
2. Description of the Related Art
It is known in the art to measure the shape of smooth metallic surfaces using laser interferometric methods. However, this method cannot be used for determining the shape of a rough surface due to a large amount of speckle appearing when illuminating a rough surface with highly coherent light. In another previously known method, the shape of a rough surface is determined by so called white-light interferometry. According to this method, light having a short coherence length is used for interferometric measurement of the shape of a rough surface (see for example WO 1994018521 A1). However, the measurement accuracy of white-light interferometry is considered insufficient. The measurement uncertainty of this method has been found to be on the order of the roughness related height variation of the test object (Theoretical measurement uncertainty of white-light interferometry on rough surfaces, Pavel Pavlicek and Jan Soubusta, 1 Apr. 2003, Vol. 42, No. 10, Applied Optics, pages 1809-1813).